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Erschienen in:
2011 | OriginalPaper | Buchkapitel
A Primal-Dual Approximation Algorithm for Min-Sum Single-Machine Scheduling Problems
verfasst von : Maurice Cheung, David B. Shmoys
Erschienen in: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Verlag: Springer Berlin Heidelberg
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We consider the following single-machine scheduling problem, which is often denoted 1|| ∑
f
j
: we are given
n
jobs to be scheduled on a single machine, where each job
j
has an integral processing time
p
j
, and there is a nondecreasing, nonnegative cost function
f
j
(
C
j
) that specifies the cost of finishing
j
at time
C
j
; the objective is to minimize
$\sum_{j=1}^n f_j(C_j)$
. Bansal & Pruhs recently gave the first constant approximation algorithm and we improve on their 16-approximation algorithm, by giving a primal-dual pseudo-polynomial-time algorithm that finds a solution of cost at most twice the optimal cost, and then show how this can be extended to yield, for any
ε
> 0, a (2 +
ε
)-approximation algorithm for this problem. Furthermore, we generalize this result to allow the machine’s speed to vary over time arbitrarily, for which no previous constant-factor approximation algorithm was known.